TSTP Solution File: SWV911-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV911-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 21:45:35 EDT 2022
% Result : Unsatisfiable 0.50s 0.69s
% Output : Refutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 24 ( 15 unt; 1 nHn; 24 RR)
% Number of literals : 35 ( 0 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 14 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(203,axiom,
equal(c_Collect(u,v),u),
file('SWV911-1.p',unknown),
[] ).
cnf(373,axiom,
equal(c_Collect(c_COMBK(c_False,tc_bool,u),u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),
file('SWV911-1.p',unknown),
[] ).
cnf(461,axiom,
equal(hAPP(hAPP(c_Set_Oinsert(u),v),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_Collect(hAPP(c_fequal(u),v),u)),
file('SWV911-1.p',unknown),
[] ).
cnf(560,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
file('SWV911-1.p',unknown),
[] ).
cnf(561,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
file('SWV911-1.p',unknown),
[] ).
cnf(562,axiom,
( hBOOL(hAPP(hAPP(v_P,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa)) ),
file('SWV911-1.p',unknown),
[] ).
cnf(563,axiom,
( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(u,v)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(u,v_c,v,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('SWV911-1.p',unknown),
[] ).
cnf(564,axiom,
( ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(u,v)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(u,v_c,v,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
file('SWV911-1.p',unknown),
[] ).
cnf(565,axiom,
( ~ hBOOL(hAPP(hAPP(u,v),v_xa))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(u,v_c,w,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| hBOOL(hAPP(hAPP(w,v),v_xb(u,w))) ),
file('SWV911-1.p',unknown),
[] ).
cnf(566,plain,
equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_COMBK(c_False,tc_bool,u)),
inference(rew,[status(thm),theory(equality)],[203,373]),
[iquote('0:Rew:203.0,373.0')] ).
cnf(606,plain,
equal(hAPP(hAPP(c_Set_Oinsert(u),v),c_COMBK(c_False,tc_bool,u)),hAPP(c_fequal(u),v)),
inference(rew,[status(thm),theory(equality)],[566,461,203]),
[iquote('0:Rew:566.0,461.0,203.0,461.0')] ).
cnf(632,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),t_a),
inference(rew,[status(thm),theory(equality)],[606,561,566]),
[iquote('0:Rew:606.0,561.0,566.0,561.0')] ).
cnf(633,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),t_a),
inference(rew,[status(thm),theory(equality)],[606,560,566]),
[iquote('0:Rew:606.0,560.0,566.0,560.0')] ).
cnf(686,plain,
( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(u,v)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(u,v_c,v,t_a)),t_a) ),
inference(rew,[status(thm),theory(equality)],[606,563,566]),
[iquote('0:Rew:606.0,563.1,566.0,563.1')] ).
cnf(687,plain,
( ~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(u,v)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(u,v_c,v,t_a)),t_a) ),
inference(rew,[status(thm),theory(equality)],[606,564,566]),
[iquote('0:Rew:606.0,564.1,566.0,564.1')] ).
cnf(702,plain,
( ~ hBOOL(hAPP(hAPP(u,v),v_xa))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(u,v_c,w,t_a)),t_a)
| hBOOL(hAPP(hAPP(w,v),v_xb(u,w))) ),
inference(rew,[status(thm),theory(equality)],[606,565,566]),
[iquote('0:Rew:606.0,565.1,566.0,565.1')] ).
cnf(758,plain,
~ hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(v_P_H,v_Q_H))),
inference(res,[status(thm),theory(equality)],[632,687]),
[iquote('0:Res:632.0,687.1')] ).
cnf(760,plain,
( ~ hBOOL(hAPP(hAPP(v_P_H,u),v_xa))
| hBOOL(hAPP(hAPP(v_Q_H,u),v_xb(v_P_H,v_Q_H))) ),
inference(res,[status(thm),theory(equality)],[632,702]),
[iquote('0:Res:632.0,702.1')] ).
cnf(782,plain,
~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(v_P,v_Q))),
inference(res,[status(thm),theory(equality)],[633,686]),
[iquote('0:Res:633.0,686.1')] ).
cnf(783,plain,
( ~ hBOOL(hAPP(hAPP(v_P,u),v_xa))
| hBOOL(hAPP(hAPP(v_Q,u),v_xb(v_P,v_Q))) ),
inference(res,[status(thm),theory(equality)],[633,702]),
[iquote('0:Res:633.0,702.1')] ).
cnf(1374,plain,
~ hBOOL(hAPP(hAPP(v_P,v_x),v_xa)),
inference(res,[status(thm),theory(equality)],[783,782]),
[iquote('0:Res:783.1,782.0')] ).
cnf(1375,plain,
hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa)),
inference(mrr,[status(thm)],[562,1374]),
[iquote('0:MRR:562.0,1374.0')] ).
cnf(1376,plain,
~ hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa)),
inference(res,[status(thm),theory(equality)],[760,758]),
[iquote('0:Res:760.1,758.0')] ).
cnf(1377,plain,
$false,
inference(mrr,[status(thm)],[1376,1375]),
[iquote('0:MRR:1376.0,1375.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWV911-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 22:43:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.50/0.69
% 0.50/0.69 SPASS V 3.9
% 0.50/0.69 SPASS beiseite: Proof found.
% 0.50/0.69 % SZS status Theorem
% 0.50/0.69 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.50/0.69 SPASS derived 579 clauses, backtracked 0 clauses, performed 0 splits and kept 644 clauses.
% 0.50/0.69 SPASS allocated 77750 KBytes.
% 0.50/0.69 SPASS spent 0:00:00.33 on the problem.
% 0.50/0.69 0:00:00.05 for the input.
% 0.50/0.69 0:00:00.00 for the FLOTTER CNF translation.
% 0.50/0.69 0:00:00.01 for inferences.
% 0.50/0.69 0:00:00.00 for the backtracking.
% 0.50/0.69 0:00:00.17 for the reduction.
% 0.50/0.69
% 0.50/0.69
% 0.50/0.69 Here is a proof with depth 2, length 24 :
% 0.50/0.69 % SZS output start Refutation
% See solution above
% 0.50/0.69 Formulae used in the proof : cls_Collect__def_0 cls_empty__def_0 cls_singleton__conv2_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3 cls_conjecture_4 cls_conjecture_5
% 0.50/0.69
%------------------------------------------------------------------------------